Archive for April, 2012


Chibikart: Finishing Touches and More Testing!

Apr 30, 2012 in Chibikart, Project Build Reports

hello internet

I’m actually not sure where the whole “Mariokart” thing that’s going around the various tech websites originated from, but rest assured that Mariokart was not an influencing factor or inspiration for this design. If anything, shouldn’t it have comically large, not comically small wheels to be considered a Mariokart? For something slightly closer to Mariokart, see LOLrioKart, a project of mine from Back In The Day.

Specific offenders: Gizmodo (and Kotaku), Buzzfeed, HuffPo, PCWorld, Daily Mail, Geekologie

Example of interesting coverage with no hackneyed Mariokart jokes: Hackaday, Wired, Redorbit


Chibikart, being a relatively quick CAD-to-completion project, is not without its share of random late-night-CADing-induced “This is TOTALLY a great idea!” moments. None of my projects are really complete without one. The first, and most immediately apparent, is this:

Chibikart’s steering linkage is made from two rod ends meeting at right angles. This presented a constraint problem since technically the majority load coming from actuating the steering connecting link (the threaded rod and ball joint) is in torsion. While using a “jam nut” fastening method worked most of the time, if anyone (namely, anyone who wasn’t me and didn’t know of this failure condition) wanged the steering too far, it would twist the black plain rod end. The result was totally changed toe angles and usually the wheels ending up pointed in opposite directions.

And then, for another example, someone running Chibikart into a wall when taking a turn too wide and just straight up shearing off the thing. I was surprised at how soft the steel alloy was. Since I deviated from my usual habit of “buy twice the amount you need” here, I was left with no replacements and also no choice but to quickly re-engineer the thing…

In a move I haven’t actively pulled since the undergrad years of yore (like maybe last year or something), I whipped up two replacements wheel mounting blocks out of solid aluminum billet in about 2 hours. These are essentially identical to the existing blocks except with a .25″ wide “ear” that sticks out the same distance as the rod end linkages did. Much better, more consistent, and it gained me another 2 or 3 degrees of steering travel  due to eliminating the big head of the rod end.

This block is also the proper height for shimming away from the upright arms. Now, none of the components rub on eachother and the steering motion is lighter than ever.

Next order of business was at least getting the rear brake parts installed. Here’s the main body of the thing with the Razor fender mounted. It pivots on a 5mm cap screw which is doubly nutted through the mounting plate. The stock Razor torsion spring keeps it sprung “up”.

It slips onto the existing wheel mounting block like so, and is retained from rotation mostly by bolt clamping pressure but I threw in the set screw locking pin just in case.

And it’s mounted. The brake will not be sticking up this far once it’s ready – I have yet to make the rolley cam thing which will actuate it. In its rest position, the top surface will be approximately horizontal.

Both sides installed. If nothing else, these are pretty neat looking fenders on their own.

Oh, so here’s a picture I forgot about last time: size comparison!

Chibikart was tongue-in-cheek designed to be “exactly the front half of tinykart“. It’s pretty close, I think.

And now, more hoonage.

Chibikart was sent up the de-facto MIT Random Contraption Proving Ground, where it completely defied (again) my expectations. The metric for performance on these tests is minimization of the energy-time product. From start to finish, the watt hours of battery energy consumed and the time taken in seconds is multiplied together. Now, the only physical unit that represents joule seconds is the Planck constant, so it’s essentially just a “score”. However, it’s a very telling score. Divide the energy consumption by the time taken and you have average wattage used in the climb (Joule / second). From the average wattage into the system you can remove estimates of motor losses (such as I^2R loss in the windings) and drivetrain losses to get an idea of the output watts. The game is one of efficiency – doing the most work while wasting the least energy and taking the least time.

Clearly, rider weight matters significantly in such a test since for the most part the You weighs much more than the vehicle.

Anyways, back to Chibikart. I managed a run that was only 62 seconds and 18.6Wh – which is on par with Melonscooter being ridden very fast, but consumed more energy – probably because direct drive magnifies motor imperfections. The total product, 1153 Whs, is actually pretty unique in the range of vehicles that have seen this test so far, and is the second best set of go-kart times (after tinykart, which holds the all-time record so far).

Chibikart pulled 1900W on launch as measured by the wattmeter, and the average draw going up the hill going by the Wh results is approximately 900W, or 225W per motor. Pretty close to the predictions. I didn’t observe any “motor unhappiness”, but that was likely due to the outside air temperature being something like 38 degrees at the time.

Here’s a Helpful Infographic made by the master of making helpful diagrams and infographics, Shane. This really needs to be zoomed in to be appreciated:

And the “initial hoonage” video:

Chibikart: The Race To Completion

Apr 28, 2012 in Chibikart, Project Build Reports

I’m happy to say that Chibikart has exceed alot of expectations.

Does this mean I finished it, finally? Yes. The build has taken in total about 3 weeks from announce to first ride test, which is rather short for one of my usually long and drawn out projects, but I was helped greatly by previously-made parts and an easy-to-assemble frame…..and not having to build a controller for it. Here’s how the remaining parts went down. The obligatory hoonage video is at the bottom.

First order of business was making the rear wheel anchor blocks. Unlike the front wheel which has tapped threads in the block (due to the need to pass the steering kingpin), the rear wheel is a fully bolt-through configuration, with the socket head 1/4″-20 bolt sitting in a counterbored hole.

With that part finished, I could finally put Chibikart on four wheels…

There was much push-riding involved. The steering was found to be very nimble and light , probably because of the very low drag wheels and high lever ratio. This thing also rolls. Because the hub motors have so little cogging and the wheel is moderately hard, it’s almost as good as a ball bearing caster wheel. I spent a few minutes finding “low spots” in the IDC lab space hallways, because Chibikart would actually start rolling towards them if pointed in the right direction.

I’m also glad to see that the wheel mounting scheme does not deflect much under even large white guys riding it (myself being relatively small and vaguely Asian). Granted, this is all on a smooth linoleum floor, and the real structural test will be when it goes outside.

Now, to do something about the baseplate upon which all the electronics will be mounted. It’s waterjet-cut from a 1/8″ polycarbonate sheet. I put in some slots for nylon/velcro strapping in order to hold the battery, and some holes to mount the Jasontrollers, but otherwise planned on freehanding all the necessary distribution electronics and other parts. I also cut out some test parts for the planned mechanical brake, but those are not yet installed.

So here’s the big generically orange block that was in the CAD model. It’s a 10S2P A123 battery module using 32113-type automotive cells. The total capacity of the pack is about 300Wh. That means Chibikart has an asston of battery for such a small vehicle. Now, while I do have giant Turnigy lithium sticks left over from the giant quadrotor of doom which are smaller by volume, this random surplus pack fit the frame so perfectly that I had to use it. It’s also more enclosed and has an internal BMS.

I didn’t take many pictures of the wiring process this time, because it’s very simple. In the upper right is a one-in-four-out terminal block which conveniently splits the battery input to exactly the number of power connections necessary. The throttle signal from the pedal gets split at a terminal block into the four Jasontrollers, each of which is otherwise only hooked up to power, ground, and motor. That’s it – 8 wires. That’s what I like about these things – they’re so bone simple yet effective.

Granted they also come with about 8,000 other wires which perform random generic electric bike functions (like pedal sense assist, cruise control, just not regnerative braking for some reason), and for all intents and purposes they don’t exist for this project.

At the pictured stage, I tried Chibikart in 2-wheel-drive mode with only the rear motors connected. As expected, starting from standstill is a little challenging because the motors have so little torque relative to my inertia. However, any movement at all is enough to cause the Jasontrollers to lock in and begin applying drive torque – even wiggling back and forth in the seat. They have quite an effective startup routine for what they are and how much they cost.

I expected that with 4 motors, it will either be better (all the motors contribute to starting torque) or totally useless (the controllers “park” the motors at the start in different directions, they fight eachother, and I have to perform an in-situ hip thrust to begin moving). Afterwards, I sacrificed some spare IEC power cords for their 18-gauge, 3-conductor hearts and extended wiring runs out to the front motors. Turns out, either situation can happen depending on where the motors stop – go figure.

I measured the current draw under acceleration at the motor for a totally stock (unmodified and unopened) 350W Jasontroller, and it was about 22 amps. Running at 32v, that means a maximum power throughput of 600W… Since the 36v native design can in fact run unmodified up to ~44v, it means that these controllers are a rare instance of some shady eBay Chinese product being underrated.

Here’s the “press shot” of the whole thing. I haven’t weighed it in yet, but it “feels” about 40 pounds. I must say I’m very pleased with the full 4-motor performance of the thing – I had expected that it would be on par with the skate motors (or at least, their very power-limited incarnation in the skates), but for some reason these are way peppier. This is probably because of their higher ampere limit (~20 amps per motor) and sliiiightly better efficiency. It remains to be seen how Chibikart handles an entire day of running outside, like at Swapfest as MIT vehicles tend to be debuted, instead of inside the cool, smooth, air conditioned hallways. Also, that lawn tractor seat is actually quite comfy.

And as promised, the video!

The short story:

  • Frame size: 34″ x 18″
  • Motors: Custom-wound and packaged direct drive hub motor, 300W peak each*
  • Wheels: 100mm 87A skate wheels
  • Battery: 32v 9Ah lithium iron phosphate pack
  • Top speed, theoretical: 26mph (voltage & motor RPM/V & wheel diameter)
  • Top speed, realistic: 21mph**
  • Actual top speed: To be determined?!
*30 second “peak” rating at 20 amperes
**Factoring in conservative estimates for air drag, and motor resistive losses at-speed, smooth and level ground assumed.


Finishing Chibikart’s Steering

Apr 25, 2012 in Chibikart, Project Build Reports

Alright, so the past few days have been spent mostly waiting on AmazonSupply McMaster orders and watering my seedlings who are now taller than I am, so I haven’t been able to tool on Chibikart as much. I wanted to get the rear two motors mounted ASAP, but working on the braking mechanism has kept me from finalizing the design for the motor mounting blocks. Therefore, I’ve been focusing more on the front wheels and getting the steering hooked up.

First, though, what the mechanical braking scheme will look like:

While I’ve certainly built plenty of vehicles which featured nonexistent or substandard mechanical braking, it’s just a bad habit to get into. I’ve decided to repurpose the Razor scooter fender brakes that I have collected through parting out quite a few scooters (and other people having done the same). Chibikart’s wheels are conveniently the same size as the standard Razor A and A2 scooter, so it was just a matter of reduplicating the mounting pattern for the brake pivot (relative to the wheel axle) on my own structure.

The more difficult part was actuation. Initially I was going to weld a steel tab or something to the steel fender to use as a pull crank for a standard bike brake cable (with return force provided by the stock torsion spring of the scooter). However, I decided to try something a little different. The cable would instead be wrapped around an offset circular Delrin (or similar plastic) cam, so if I pull the cable, the cam swings down and pushes on the brake. The (rather stiff) torsion spring provides restoring force. This execution ended up being alot cleaner than the design which involved the mysterious welded bell crank. Also, sweet rear fenders.

Onto steering!

Yes, that’s a Kurt vise speed handle. I found it eBay for like 10 bucks, and it was essentially the correct size and everything!

The steering column itself is made from a section of 3/4″ OD, 0.040″ wall chromoly tubing, droppings from the FSAE racing team. I sandpaper-finished the tube on a lathe to take it to the proper slight undersize in order to fit into the steering bushings. A 3/4″ steel hex shaft cutoff was machined down to the ID of the tube, and is retained via a clamping shaft collar.

Chibikart’s steering is just a tower of shaft collars. The leftmost one is a bottom retaining collar and prevents the shaft from being pulled upwards. The one to the right has a built-in mounting flange that I used to attach my “Pitman arm”, the driving link in a standard linkage steering setup. I wish I had known about these things when making a certain other kart’s steering arm. That one was more metal than I think exists in this entire frame.

finishing those damned motors

Over the past few days, I also had a few stretches of 100% HARDCORE NONSTOP MOTOR WINDING. Finally knocked all those motors out… My hands are unhappy, but nowhere near as bad as when I had to wrestle 20 and 22 gauge solid – that stuff takes more tension to get right, where as much of the wire tension on this build was supplied by my little winding jig.

The motor torque constants are scribbled on their cans. As I finished each motor, I lathe-o-mometerd it to obtain its BEMF profile, and the Kt was estimated from that.

Back to steering. Here’s one of the “swivelly block axle anchoring doobobs” which I’m sure have a real name I cannot remember at the moment. They are simple chunks of milled aluminum with a 1/2″ hole through them. A 1/2″ steel pin with threaded ends fits in the hole, and it rides in the flanged R8 bearings. There is no torque transmission to the axle at all – it’s just a slip fit, since the linkage will push on the block directly. I installed around 0.1″ of shims in between the block and the R8 bearing, but I’ve found out that this is not enough – under the weight of a rider, the aluminum block still digs into the plates above and below it!

The reason seems to be that adding shims to the stack seems to only succeed in pushing the bearings out of their holes. I should have designed with the flanges on the inside to prevent this – it seems obvious now, but it’s definitely a manifestation of 5am Engineering Syndrome of which I am probably the patient-zero for.

The linkage itself is bone simple. Those chromate plated ends are control rod ball joints which are convenient because they have a right-angle stud ready to bolt into a linkage. The arms on the axle blocks themselves are “square shoulder plain rod ends“, screwed into the blocks and then locked in place with a jammed nut. The linkage proper is a section of 1/4″-28 B7 threaded rod, not even in tension-compression arrangement.

I like this linkage alot. It gets the point of steering linkages across while being simple to build. The downside is it that is not a true Ackermann style steering linkage – to get that kind of inside-wheel-turns-more behavior, the wheels must be positioned further out so the steering arms could be mounted inboard from the steering kingpin, a design tradeoff I wasn’t willing to make. It is approximately Ackermann for the extremes of its travel because the center linkage is shorter, causing one side to approach toggle quicker than the other.

What I learned while making this linkage was that nylock nuts are in fact nuts in a shell. I needed a non-locknut in 1/4″-28 really quick, and wasn’t sure where to find them. However, I had a bag of 1/4″-28 locknuts. I machined off the nylon part in hopes of finding a plain nut, but instead I discover it’s a threaded insert inside a formed steel shell!

Now, maybe not all nylocks are like that, but this was one of those “oh so that’s how they make it” moments.

No, I still haven’t figured out how they got the ball inside the ball joint.

After receiving my order of axle bolts, here’s one of the front wheels mounted!

I tried to sit on this 2-wheeled arrangment (2 front wheels) and tested the steering, which is when I discovered the scrubbing problem. I’m realizing that “more shims” isn’t the answer in this case. I’ll either have to flip the plates (bearings on the inside) and shave 1/16″ off each side of the blocks, which may or may not actually be possible, or perhaps just mill off a thin layer of everything but a small section in the center to make a virtual shim without changing the thickness of the block substantially.

Or just, you know, pour cutting fluid into it and let it sort itself out.

Next up on Chibikart, attaching the baseplate, making the last two wheel mounting blocks, and throwing some electrons at the thing!

Chibi-Everything, Part II: Copter

Apr 21, 2012 in Chibicopter, Project Build Reports

Poor Chibicopter.

So I’m proud to announce that I’ve found a solution to the XBee over-the-air code uploading problem. The only catch is that…

…it involves chopping an FTDI cable header onto the board.

Yeah, not groundbreaking or world-changing. But, at least I’ve gotten over my software-induced project fear stage and now have a workable, if slightly convoluted, procedure for uploading code and debugging! The hookup for the FTDI is essentially that of the Sparkfun Pro Mini, but instead of DTR I have RTS from the standard FTDI cable going into my reset isolation capacitor thing.

I really should have just done this like two weeks ago.

Anyways, here’s a picture of me triple wielding XBees in order to get this thing to work. The current signalling protocol is:

  • The Xbee connected to my transmitter (in bypass mode) is address 2, the XBee on Chibicopter is address 1, and my debugging/base station is address 0
  • XBee 2 only transmits to Xbee 1 (ATDL = 1 ATMY = 2)
  • Xbee 1 only transmits to Xbee 0 (ATDL = 0 ATMY = 1)
  • Xbee 0 transmits to the nonexistent XBee #3 (ATDL = 3 ATMY = 0) in order for its serial transmissions to not appear on the others
  • Therefore, my radio transmits commands to Chibicopter, which in turn transmits debugging data to the base station where it appears on my screen.

To reprogram Chibicopter, I remove the Xbee from Chibicopter, disengage the base station XBee adapter and jam the FTDI cable onto Chibicopter. I have to take the XBee onboard out first because there is no selection/domination circuitry which allows both XBee and FTDI cable to use the serial lines at the same time.

It’s quite an overloaded process, but it has at least gotten me to the point of…

…being able to finally read the pulsewidths from my radio. All four of the ones I care about. The Serial buffer reading code needed a bit of tweaking – I had to flush the serial receive buffer after every read or else it would desynchronize because more packets appear as the procedure was executing.

Sadly enough, there is no more Serial.flush() in Arduino 1.0, the functionality having been removed. I wondered why briefly before just writing a dumb serial buffer clearing loop.

Anyways, the good news is that I transferred enough core functionality over from tinycopter such that Chibicopter’s props respond properly to suddenly orientation changes! That means it’s just some tuning of gains away from actually flying.

The bad news is that through some irony of fate, two of the tiny 1S-lithium motor controllers have ceased to function. Just in time, right? I’m uncertain as to why they failed. One possible reason is that since the board has absolutely no logic power supply at all (everything running off the 3.something volt battery) that 5 volts from the FTDI cable was enough to destroy the weaker ones.

Now, I’m also wondering why it is that there is an option for 3.3v-compatible logic but with 5 volt VCC (power supply). If the point is to use it with a 3.3v system safely, isn’t this undesirable?

No matter – I have more spares on the way, but they’ll still take a few days to arrive. In the mean time, I might make a little pass-through board or something which down-regulates the 5v USB power to 3.3v.

and then it will fly I swear guys



Chibi-Everything, part I: Kart

Apr 20, 2012 in Chibikart, Reference Posts

A double-update from the term of smaller and cute projects! First, I’ve discovered to little surprise that Chibikart will have no torque whatsoever. And second, I’ve finally gotten over my fear of XBees to mine Chibicopter back out from the pit of paused project despair in order to… attach an FTDI header to it. Oh, the backpedaling.

First, why Chibikart will be a super laid-back performer.

Last time, in testing the mostly-36-turn motor, I found out that my back-EMF (/torque) constant was a dismal 0.126 Nm/A. This was off from the predicted 0.19 Nm/A and even down from the single-winding guessed 0.16 Nm/A. There were probably two major factors involved. First, I could not stuff 36 turns onto all of the windings at all. Not even close. Besides A-phase, the rest of the phases more realistically have about 30 turns per tooth. Just this small (16%) reduction isn’t enough to explain the drop from 0.19 to 0.126, though. I’m also suspecting that the 3 little toothlets on each tooth increase my apparent air gap (since only parts of them are at the design airgap) and the rest are about 0.75mm inwards – the airgap in that area is about 1.25mm.

The depressions and raised tooth areas each occupy about half the area of the tooth, so the average airgap would be 0.875mm for one tooth.  The maximum theoretical flux density at this average surface is therefore (1.2 tesla for N42 grade magnets) * (2mm thickness / (2mm thickness + 0.875mm airgap)) = 0.83T. If the airgap were evenly 0.5mm throughout (which is the design gap), then the average flux density rises to 0.96T. The 13.5% loss of the field strength from 0.96 to 0.83 coupled with the 16% loss of winding turns means that (0.19 Nm/A) * (0.865) * (0.83) = approximately 0.136.

Plus or minus some second-order effects and nonidealities, and I think the lesson is clear – real life sucks. That, and I need to find a better stator.

The second motor was even worse.

Through more test winding, I found that 27 turns was what I could reliably wind on one tooth. Meaning very little “cancerous bunching” as seen in the first motor winding picture, and which could be completed reasonably fast without being messy. It turns (!) out that keeping the wire under high tension the whole time improved packing alot – go figure – and I added another zip tie to my winding jig as a result.

Unfortunately, 27 turns is even worse than 30 turns. The above scope capture is the lathe-o-mometer signature of the second Chibikart motor. The calculated BEMF constant is an even more depressing 0.11 Nm/A. While consistent with an incremental (27/30) decrease in the turn count, it’s still…. so soul-crushing.

By this time, I was seriously questioning if the first generation skate motors which these things are based off of ever reached their design 0.26 Nm/A. It seemed impossible given my above results. The skatemotors were true 36 turn (but single 24 gauge winding), so based on the results I got with the first motor, I should see a realistic Kt of 0.15 Nm/A.

How did I find out? Well, I had to temporarily put the left RazErBlade on blocks to find out – I removed the motor and shoved it on Tinylathe. Another problem was that in this design, the wires ran out through the center of the motor, meaning Tinylathe couldn’t grab onto it at all.

Fortunately, a DeWalt 18v drill in high gear saved the day.

This motor’s waveform is a bit more erratic, but the average voltage magnitude is about 4.5 volts at 62 Hz. This gives a Kt of…. 0.08 Nm/A? Did I wire up this motor backwards?!

Something wasn’t right. I decided to declare this test bogus and just try running the motors using an ESC. I used Melon-scooter propped up on a table as a test jig – it has a 500w type Jasontroller right now, which is very representative of what the final control solution will be, so what better basis for comparison? A laser tachometer was used to record the no-load speed of the motors, and I used a 15 amp power supply set to 33 volts with maxed out current – the no load test shouldn’t result in such high currents anyway.

These results were telling.

  • Chibikart motor 1, ~30 turns, achieved a no-load speed of 2671 (Oh the irony) RPM on 33.0v for a RPM/V (classical “Kv” rating) of 81, and a calculated Kt of 0.118.
  • Chibikart motor 2, ~27 turns, achieved a no-load speed of 3036 RPM for a RPM/V of 92; Kt of 0.103. This is almost exactly the ratio of 30/27. Universe still makes sense: “Kv” is essentially the inverse of Kt, so a higher RPM/V is less Nm/A.
  • Skatemotor, ~36 turns, hit 2078 RPM for a RPM/V of 63 and Kt of 0.151. Well hey.

The ratio of turns alone, 36/30, does not account entirely for the discrepancy – it alone would calculate a Kv of 68 RPM/V using Chibikart motor 1 as a basis. While the difference of 5 RPM/V is certainly within the realm of “bah, close enough”, I think the shape of the tooth and arms is a major higher-order effect that linear models like “T = k*NBLR” doesn’t capture. The original skatemotor stators did not have those stupid toothy things.

Now, why is Kt (calculated) different from Kt (measured-with-oscilloscope-and-lathe)? I should probably mention that Kt changes with the type of drive input (sinusoidal, 120 degree trapezoidal which is the standard, 180 degree trapezoid…) and the phase of the drive input (advanced, retarded, etc.). This is something I kind of sweep under the carpet when explaining How Moter to someone because it’s very mathematical in nature, so for your amusement, here is how moter for real and how2controlmoter.

If I can hold 27 turns on each motor from here on out and maintain 0.11 Nm/A, then Chibikart will have a maximum launch force at 20 amps of 4 * (20 A * 0.11 Nm/A) / 0.05m wheel radius, or 176N at-ground linear force. I chose 20 amps as a reasonably burst rating because not only is it roughly what a stock 350W-type Jasontroller outputs without modification, but to heat up a roughly 80 gram (estimate of the total winding weight*) copper chunk from 20C to 200C, the maximum temperature rating of the magnet wire I used, at 20 amps will take about 30 seconds. The actual math: (0.384 Joules/(gram-Kelvin) for copper [1] * 180K thermal differential * 80 grams) / (20 amps ^2 * 0.37 ohms resistance of the 27-turn motor line-to-line) yields about 37s.

Why 30 seconds? Because I have to put a definition down somewhere. This is why “burst vs. continuous” ratings are bullshit if no time period of overload is given. I could reasonably pump 40 or even 50 amps into these motors for a quick launch, but they’d heat up reeeeeeeeeeeal fast if I tried to push that current continously. 30s is a generous estimate, since my magnets would be long-gone at 200C… even 80C will be enough. (However, the magnets are not in direct thermal contact with the copper, so I can certainly flame out the windings with overcurrent before any other damage is suffered)

So the bottom line is don’t expect Chibikart to behave like tinykart. With ~180N of maximum launch force, I’ll get a maximum acceleration of about 2 m/s^2. Which I guess isn’t that bad, but yeah. It will also not be happy at all going up the de-facto vehicle proving ground.

There’s so much random math in this post that it must be of some use to someone, so I’ll lob this under “Reference Posts” too.

* Each turn on a tooth is assumed to have an average dimension of 21mm length and 10mm width, for a total perimeter of 62mm per turn. There are 27 turns of 6 strands of parallel wire, so on each tooth is 10.04 meters of wire. There are 12 teeth, so the total length of wire in a motor is about 121 meters. In feet, that is 395 feet. #28 gauge magnet wire is 2028 ft/lb so the total mass of copper in each motor is .19 lb – or 3.11 ounces, or about 87 grams.